KL Dra as a Benchmark Laboratory for Accretion-Disk Physics: Constraints from TESS and Ground-Based Surveys

We present the longest-term optical analysis of the AM CVn system KL Dra using $\sim11$ years of monitoring from TESS and wide-field ground-based surveys. The continuous TESS coverage allows us to characterise its frequent outbursts with unprecedented detail, providing the first comprehensive study of an AM CVn during outbursts and enabling detailed modelling of these systems. The superoutbursts in KL Dra generally include a precursor, and are followed by a series of rebrightenings after which a sequence of 3-4 large amplitude normal outbursts is observed. We fit parametric profiles to each superoutburst component (precursor, rise to plateau, plateau, decay), to rebrightenings, and to normal outbursts, which let us quantify every high state feature and investigate correlations with the system's long term supercyle evolution. Our continuous coverage reveals an average value for the supercycles, superoutbursts and normal outbursts of $60.4 \pm 0.1$ d, $5.67\pm0.03$ d and $1.17 \pm0.01$ d, respectively. The supercycle duration may be correlated with the rebrightenings duration and superoutburst amplitude, and anticorrelated with the plateau length. Within a supercycle, normal outbursts grow in amplitude and duration, and the first normal outburst is usually highly asymmetric, while subsequent normal outbursts are more symmetric. We detected superhumps in TESS superoutbursts but not in the rebrightenings or normal outbursts. We interpret the results within the disk instability model, considering additional effects, such as changes in the donor mass transfer rate.